The prop will join the team after next year's World Cup in France where he is expected to be a Springbok regular after helping South Africa to win the last World Cup in Japan in 2019.
"His set-piece excellence and the physical edge to his play will, together with his winning mindset, be a real asset to us when he joins us next season, and we look forward to welcoming him to the province," said Ulster coach Dan McFarland.
Kitshoff will complete the current season with the Cape Town-based Stormers, who won the United Rugby Championship last season and for whom he has made 122 appearances since his debut in 2011.
It will include a trip to Belfast in January to take on Ulster in the URC.
Ulster this season signed veteran South Africa loose forward Duane Vermeulen (36), who was also a key member of the World Cup-winning outfit but has since lost his place in the Bok squad.
